Low entropy 3 mins from big bang query

The title pretty much sums up what I am not comprehending. At about the time when atoms stopped forming I am asked to accept that this initial state of the universe was at an exceedingly low state of entropy.

Apparently it is due to the immense gravitational force. However my understanding so far of entropy is that one can change bits around without it affecting the general disorder.

So even with this large gravitational field, we still have a universe which at that time would be an homogenous soup of H and He. I do not see how suddenly this homogenous plasma which is as disordered as an homogenous box of H and He gas would be at room temp can survive the general definition of entropy.

Is it that the definition of high entropy given above is wrong. Or is it that gravity is the opposite of entropy? Is the relationship between gravity and entropy analogous to the relationship between kinetic and potential energy?

So are you saying that the real low initial entropy state would be just before the moment of inflation rather than the 3 minute mark? Or is the 3 minute mark still considered to be low entropy due to the relative smallness of the volume compared to the current volume.

So are you saying that the real low initial entropy state would be just before the moment of inflation rather than the 3 minute mark? Or is the 3 minute mark still considered to be low entropy due to the relative smallness of the volume compared to the current volume.

So are you saying that the real low initial entropy state would be just before the moment of inflation rather than the 3 minute mark? Or is the 3 minute mark still considered to be low entropy due to the relative smallness of the volume compared to the current volume.

To me, 'low entropy' , 'high entropy' are meaningless. Entropy increased at every time, including during inflation.

This is, in general, a complex question. But one simple part of it is that in a larger volume there are many more quantum states than a smaller volume. The simple act of expanding increases entropy.

Excuse me for being a bit simple-minded about this. I read the FAQ explanation. I also viewed Penrose's lecture, Misner's 1969 paper and John Baez's explanation. These last three were over my head, although I could relate some of what Baez said to parts of the FAQ explanation.

As I understand it, entropy is a measure of the energy that's not available to do work.

Thus, in the far distant future if all nuclear reactions have ceased, all gravitationally bound systems have either collapsed or irreversibly dispersed due to the expansion of the universe, and the background radiation has reached thermal equilibrium - the universe will have maximum entropy. There will still be plenty of energy in the universe (as much as it started with, I suspect), but none of it will be available to do work of any kind.

I hope I'm right so far because I think I understand this concept pretty well.

If we go to the other end of the scale - and the OP - the question seems to be: If the universe was very nearly homogeneous and isotropic (although very hot) shortly after the big bang, why wasn't the entropy high at that point in time also?

At this point I'm trying to piece together the FAQ explanation (to which you and bcrowell were contributors) with your statement quoted above. Specifically, the following portion of the FAQ explanation:

If we psssssht a bunch of helium atoms into a box through an inlet valve, they will quickly reach a maximum-entropy state in which their density is nearly constant everywhere. But in an imaginary Newtonian "box" full of gravitating particles, we get the opposite result, provided that the particles have some mechanism such as radiation for releasing energy into the environment. The final state is one in which the particles have all glommed onto each other in a single blob. The blob's entropy has decreased, but this decrease is more than counteracted by the increase in entropy of the environment.

I can vaguely understand Baez's collapsing gas cloud explanation that the shrunk down cloud has a higher temperature, but the overall entropy of the space occupied by the original cloud has decreased (at least that's what I think he's saying).

I can also understand the Newtonian "box" concept in the FAQ example, which is similar.

Your statement "...But one simple part of it is that in a larger volume there are many more quantum states than a smaller volume. The simple act of expanding increases entropy..." makes me think, though.

A homogeneous and isotropic compact cloud of (hot) gas has low entropy. If it expands to a larger homogeneous and isotropic cloud of (cooler) gas (and stars and planets) it has higher entropy.

This sort of brings me back to the question posited in the OP: "... Is the relationship between gravity and entropy analogous to the relationship between kinetic and potential energy?"

Is the amount of entropy inversely proportional to the strength of the gravitational attraction all the "stuff" in the universe exerts on all the other "stuff"?

To put this another way - and I hope I'm using these concepts correctly - cosmologically speaking, does the increasing volume of an expanding universe cause the stress-energy-momentum tensor in the Einstein Field equations to decrease? Is it this decrease that results in the increase in entropy?